Swedish patent application 8207099-6 discloses a filter device in the form of an integrated bag unit consisting of a coarse filter bag and a fine or microfilter bag enclosing the coarse filter bag. An essential advantage of this filter device is that the coarse filter and the fine filter can be dismounted and disposed of as a single unit. It has however proved difficult to give the coarse filter bag or layer such a fibre structure that it will intercept and separate only the relatively coarse constituents of the air stream while letting through the finer constituents to the fine filter layer. Thus, both the coarse and the fine constituents jointly tend to be agglomerated in and on the coarse filter layer so as to cause premature clogging thereof. As a result, the whole filter device will have a short service life.